A195110 - OEIS

%I #5 Mar 30 2012 18:57:44

%S 1,2,1,2,3,1,4,2,3,1,4,5,2,3,1,4,5,6,2,3,1,7,4,5,6,2,3,1,7,8,4,5,6,2,

%T 3,1,7,8,9,4,5,6,2,3,1,7,8,9,10,4,5,6,2,3,1,11,7,8,9,10,4,5,6,2,3,1,

%U 11,12,7,8,9,10,4,5,6,2,3,1,11,12,13,7,8,9,10,4,5,6,2,3,1,11,12

%N Fractalization of the fractal sequence A002260. Interspersion fractally induced by A002260.

%C See A194959 for a discussion of fractalization and the interspersion fractally induced by a sequence.  The sequence A002260 is the fractal sequence obtained by concatenating the segments 1; 12; 123; 1234; 12345;...

%t j[n_] := Table[k, {k, 1, n}]; t[1] = j[1];

%t t[n_] := Join[t[n - 1], j[n]]   (* A002260 *)

%t t[12]

%t p[n_] := t[20][[n]]

%t g[1] = {1}; g[n_] := Insert[g[n - 1], n, p[n]]

%t f[1] = g[1]; f[n_] := Join[f[n - 1], g[n]]

%t f[20] (* A195110 *)

%t row[n_] := Position[f[30], n];

%t u = TableForm[Table[row[n], {n, 1, 5}]]

%t v[n_, k_] := Part[row[n], k];

%t w = Flatten[Table[v[k, n - k + 1], {n, 1, 13}, {k, 1, n}]] (* A195111 *)

%t q[n_] := Position[w, n]; Flatten[Table[q[n], {n, 1, 80}]]  (* A195112 *)

%Y Cf. A194959, A002260, A195111, A195112.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 09 2011